Artificial line.



R. S. HDYT.

ARTIFECIAL UNE.

APPLICATION FILED nus. 7. 19:5.

Patented Jan. 11, 1916.

Ingegtorg: R. 0y

UNITED STATES PATENT OFFICE.

BAY S. I-IOY'I, OF BROOKLYN, NEW YORK, ASSIGNOR TO AMERICAN TELEPHONE AND TELEGRAPH COMPANY, A CORPORATION OF NEW YORK.

ARTIFICIAL LINE.

Specification of Letters Patent.

Patented Jan. 11, 1916.

Application filed August 7, 1915. Serial No. 44,173.

' the following is a specification.

My invention relates to an artificial line for simulating the impedance of a long periodically loaded transmission line over a preassigned range of frequencies, as, for example, over the range of frequencies necessary for the telephonic transmission of speech. It constitutes an improvement over my previous invention disclosed in Patent #1,124,90-1, dated January 12, 1915, in that my present invention takes into account the distributed character of the line inductance, that is the fact that the line inductance is distributed, and, as a further refinement, it also takes into account the effect of the line and load resistance on the impedance of the loaded line. My present invention, therefore, simulates to a still higher degree of precision the impedance of the actual transmission line.

In the accompanying drawing, Figure 1 illustrates diagrammatically a basic form of artificial line arranged in accordance with my present invention; Fig. 2 shows a modification of the invention, providing what may conveniently be termed a consolidated form; Fig. 3 illustrates a supplementary structure for taking into account the effect of line and load resistance; Fig. 4 shows the complete structure obtained by combining the structures shown in Figs. 1 and 3; and Fig. 5 presents a series of curves showing the precision with which my invention,

as embodied in Fig. 1, simulates the impedance of the actual loaded line.

By comparing Fig. 1 of the present application with Fig. 1 of my above mentioned patent, it will be noted that in lieu of the resistance element R shown in the drawing of the patent, my present invention provides a resistance R shunted by an inductance coil L and a condenser C in series. The function of the L C shunt is to give the resistance component of the impedance the drooping characteristic, shown by Fig. 3 of my previous patent, which the resistance component of the actual linejmpedance has. The L C shunt gives rise, however, to a reactance component, and this reactance component is neutralized b the L C portion of my present invention. The L 0 portion 0 my present invention simulates the reactance component of the actual line impedance; its function is therefore the same as that of the L C portion of my previous invention. In addition to these differences between my previous and my present invention, the latter is more pre cisely proportioned to take into account the distributed character of the line inductance. and, furthermore, the supplementary structure of -Fig. 3, which comprises an inductance coil L in series with a condenser (1,, takes into account the efiect of line and load resistance, an effect entirely ignored in my previous invention.

Having thus briefly pointed out certain differences between the present invention and that over which it is an improvement, I will next point out the fundamental principles underlying my present invention and the manner of applying said principles so as to provide a structure having the aforementioned distinguishing characteristics.

A general formula for the mid-load impedance of a long periodically loaded transmission line (see equation 19 of G. A. Campbells paper On Loaded Lines in Telephonic Transmission, Philosophical Magazine, Ivfarch, 1903) is:

The above formula is the same as that given in the above mentioned paper except for a slight change of notation consisting in substituting the symbol q for Hd, m for and s for d. It is also equivalent to the formula given in my previous patent, as is shown in the said Campbell paper. This particular formula is chosen as more convenient in deriving approximations. In the notation thereof, K denotes the mid-load characteristic impedance of a periodically 'i= /1;andp=21rf, where 7 denotes the frequency in cycles per second.

The value of m in equation (1) is ex pressed by the following equation:

The above equations (2) and (3) are familiar ones and are found in standard treatises on the theory of transmission lines.

By modifying the above-given fundamental formula (1) in the manner now to be described, approximate formulae of high precision may be derived, by the aid of which the artificial line of my present inven- 'tion may be constructed. In my above-mentioned patent it is stated that the mid-load characteristic impedance of the loaded line is very closely equal to the impedance of a loaded line having no leakage conductance, no resistance and no distributed inductance, but having the same total inductance L and total capacity 80 per section as the actual line. In accordance with these approximations the mid-load impedance K is very closely expressed by the equation where T is equal to \[T JECIII and w=p It is also shown in my previous patent that the impedance of a line beginning not at mid-load but at a distance ms from the first loading coil can be approximately 1--4a:(l:o)w where a: denotes the fractional length of vthe first section.

Formulae (4) and (5) are in substance identical with the formulae given in lines 16 and 39, respectively, of page 2 of my abovementioned patent, diflering slightly therefrom in form owing to certain changes and improvements in notation.

It will be observed that the impedance formula: expressed by equations (4:) and (5) ignore entirely the small effect produced by the actual resistance of the line and. of the load coils and further that they neglect the distributed. character of the line inductance in that the total distributed inductance of each loading section is lumped and added to the inductance of the corresponding load coil. The errors introduced by these assumptions, while small, are not always negligible and in the artificial line of my present invention I desire to take into account the elfects produced by the resistance of the line and of load coils and also the distributed character of the line inductance. To this end I have derived more closely approximate formulae in a manner now to be set forth. Since the impedance effects produced by the distributed character of the line inductance and by the resistance of the line and of the load coils are small, in deriving formulae to take into account said effects, I have considered each of said effects separately and have obtained the joint eifect by superposition.

Referring to equation (1), if the load coil is considered as having inductance L only and the line as having distributed inductance J and distributed capacity C per unit length only, that is if the resistance of line and load, as well as leakage, are neglected, it follows from the definition of symbols hereinbefore given and from equations (2) and (3) that q tpL m i1) J56 and that equation (1) reduces to 7 that is the square root of the ratio of the line inductance per loading section to the inductance per loaded coil. A further direct mathematical transformation reduces equation (7) to the form Equation (8) shows that K vanishes if and that, by the introduction of a coefiicient b it can be exactly expressed as The coefiicient Z) is closely, but not exactly, equal to Rigorously it is a function of 'w and therefore of the frequency. It varies, however, very slowly with the frequency. Moreover, if any particular frequency is specified, b is determined by equation (9) in terms of the value of 80 corresponding to said frequency and in terms of the parameter 1:. 1f the coefficient b is so determined, equation (9) will be very closely,'though not exactly, correct for other values of the frequency. The departure from equality of said equation is, however, very small within the range of frequencies of practical importance.

It is convenient and desirable, for reasons of simplicity, to determine the value of l), as given by equation (9), for the smallest real value of w, or of the frequency, for which K vanishes. As liereinbefore stated K vanishes, as shown by equation (8), when 1 :10 tan. ow

e 0 v y 1. 0000 .0529 .9913 .0900 .9852 (11) .1369 .9778 1936 .9689

Other values of w Within this range can be gotten from table (11) by interpolation.

Returning to equation (7), substitution I The coeflicient b has been so chosen that (12) is exact for 'w ui it therefore follows from (12) that rra 1 b and that:

Denoting T41 '0 by T and equation (13) reduces to K=T /1w (14). Equation (14), giving the characteristic mid-load impedance of the loaded line, corresponds in form with equation (4), with the difference that T is substituted for T and 10,, for 10. If two parameters L and C are introduced, such that it follows from a reference to the expressions which T and 10,, represent, that I Reference to the significance of the previously employed symbols T and 10 show that T and w, are of the same form as T and 10 respectively, differing only in the substitution of L for L and C for O, as given by equations (15) and (16).

Equation (14) is a highly precise expression for the characteristic mid-load impedance of a loaded line. The precision thereof is higher than that of the corresponding equation (4) in that in equation (14) the distributed character of the line inductance is taken into account. The characteristic impedance of a loaded line having an initial section of length ms is derivable from equation (14) precisely as equation (5) is derivable from (4) and is given by parts of the right-hand side of equation (19).

Equations (14) and (19) express the characteristic impedance of a loaded line having no resistance. actual resistance in modifying said formulae is now to be shown. In investigating this effect, which is known to be quite small, as hereinbefore stated, it is allowable, at a very small sacrifice of precision, to assume that the loaded line to be simulated has no distributed line inductance but a load coil inductance L and a distributed capacity C0 per unit length of line. It is further allowable to assume that the resistance R of the load coil is added to the distributed resistance R of the line, giving an apparent K=T mo if This equation, in which the symbol 9 denotes is directly derivable from equation (1) in Equation (26) differs from equation (14) only in the addition of the imaginary term. It will be seen that the actual resistance of the line and load coil produces a quite negligible effect on the real or resistance component ofthe impedance, but that it does produce an appreciable efiect on the imaginary or reactance component of said impedance. It may be then stated that the effect of line and load resistance on the characteristic impedance of the loaded line is taken into account if to equations (14) and (19) a termz'y is added, such that In equation (27) sr, as hereinbefore de- The effect of the.

distributed resistance r per unit length of line,

Referring to equations (2) and (3), substituting r for R, C, for C, and setting .1 and ii equal to zero, the values of k and m i reduce to #395; coth Jtfiwg (24).

accordance with the assumptions hereinbefore stated. It

coth Jigib;

is replaced in (24;) by its equivalent series, and if negligible terms thereof are dropped, equation (24) reduces to fined, is the total resistance per loading section; that is the resistance of the line of length .9 plus the resistance of one load coil.

My invention in the light of the foregoing discussion will now be understood to consist in providing a simple circuit arrange ment which shall have over the range of frequencies between the limits corresponding to 111 0 and w w the impedance expressed by equation (19) and, as a higher refinement, that given by adding the ex pression (27) to (19), as will now be more fully described.

The circuit arrangement which simulates the impedance expressed by formula (19) may conveniently be termed the basic struc' ture and is shown in Fig. 1. The part consisting of the inductance L in parallel with the capacity C simulates the reactance component Q of Z as given by equations (19) and (20). Referring to said equations it will be seen that the imaginary or reactance component may be written The impedance of an inductance L, in parallel with a capacity C is well known to be expressible as 1 L C p' Comparison of this expression with equation (28) shows that they are identical provided that L and C be given the following values:

It is thus seen that the L C portion of the basic structure simulates the reactance component of the impedance of the loaded line provided that L and C are proportioned in accordance With equations {29) and (30).

Equations (19) and (20) show that the resistance component of the characteristic impedance of the loaded line is given by Referring to the curves shown in Fig. 3 of my above mentioned patent, it will be seen that said resistance component for values of .22 less than .17 has a drooping characteristic and finally becomes zero at w l. Now a resistance element shunted by an inductance element and a condenser in series will have a similar resistance characteristic provided that the inductance-condenser shunt is resonant in the neighborhood of 10:1. The impedance of a resistance R in parallel with an inductance L and a con denser C in series is Well known to be il l PfLi 1 11 1 1 1 Here A and B are, respectively, the real and imaginary components of the expression on the lefthand side of equation (32), and are therefore the resistance and reactance components respectively of the impedance of said combination. If an equation(32) =A +iB 32 is substituted for its identity 2, the values Proceeding then on the assumption that the resistance component of the impedance of a loaded line having an initial sectional length of 0.17 or less might be simulated by the resistance component A of a resistance element R in parallel with an inductance L and a condenser G provided proper values were assigned to w and B L C I 'performed an elaborate series of computations and plottings. The general character of these computations was to assign tentative values to the parameters 00, R L and C compute the corresponding values of D as given by equation (31) and A as given -by equation (33), plot curves with said values as ordinates and 10 as abscissa and compare said curves. By such means I discovered that the desired simulation Was attained over the required range from 10 :0 to 10 :1 by assigning the following values:

E 1 Va Fig. 5 serves to show the high degree of precision with which the resistance component A approximates the resistance component D of the line impedance. In said Fig. 5, the curve 1 is a plot of the resistance component of the actual loaded line with an initial section of .148, While the curve 2 is a plot of the resistance component A of my artificial line, the abscissae being the values of 0 Equations (36), (37), (38), are then the design formulae in accordance with which I proportion the R C portion of the artificial line.

The reactance component B must be neutralized since it does not usefully simulate any component of the line impedance. This neutralization is accomplished very closely, as hereinbefore stated, by adding to the R L C portion of the structure an inductance coil L in parallel with a condenser C provided that, as determined by computations and comparison of the expression for B and the impedance of an inductance in parallel with a condenser,

L2: .120 L 39 o (128)8'0 (40) The precision with which the reactance of the L C portion neutralizes the reactance of the R L. C portion is shown in Fig. 5, in which curve 3 is a plot of B and curve 4 is a plot of the reactance of the L C portion of Figs. 1 and 4, wherein w=O.14. If 12:0.14, the value hereinbefore assigned to it, equations (29) and (30) become C (.3344).5 C (42) If then the elements of the structure shown in Fig. 1 are proportioned in accordance with equations 35-42 inclusive, the structure simulates very closely over the entire range of frequencies necessary for telephonic transmission of speech, the impedance of the loaded line having an initial length of line equal to 0.14 of the length of a loading section. This is illustrated in Fig. 5 in which the resistance simulation is shown in curves 1 and 2, already referred to, and in curves 5 and 6 which are plots of the reactance component of the actual loaded line. and of the reactance component of the structure shown in Fig. 1, respectively.

It will be noted that the basic structure designed in accordance with the design formulae (35) to (42), inclusive, simulates the characteristic impedance of a loaded line having a particular initial length of line equal to 0.14 of a loading section, since the simulation is most precise for this particular value of the initial length ms. In general, of course, the line may have any length of initial section, so that it becomes necessary to supplement the basic structure to the end that it may simulate the impedance of a line of any initial length ms. This may be accomplished in the manner stated in my above-mentioned patent, as for example by addingrto the artificial line an extension, so that the extended artificial line shall be equivalent to a line having an initial length :rs. It will be understood that such extension may likewise be proportioned. in accordance with L and 0,, whereas in my pre vious patent the extension was proportioned in accordance with the values of L and C.

If it is desired to take into account the resistance effect as given by equation (27), there should be added in series with the basic structure an inductance coil L, and a condenser C, in series, whose values are:

The impedance of this combination, L, in series with C is well known to be Substitution of the above given values of L and G and comparison of the impedance of this arrangement with that given by equation (27) shows that they are equal.

A simplified form, which may conveniently be termed the consolidated artificial line, can be gotten from the basic structure at a very small sacrifice of precision of simulation by combining the L portions into a single L, C, portion, as shown in Fig. 2, and this constitutes a particular simplified embodiment of my invention. By

C and L G, 1

computations analogous to those by which the R, L C, portion is obtained, the most suitable values of L and C are given as follows:

L,: o.iss)L, (45

This invention, as in the case of the invention disclosed in my aforementioned pattent, finds its application where the impedance of a loaded line is to be Simulated, as for example, for balancing purposes in systems involving two two-way telephone re peaters and in other transmission lines. Suppose, for example, it is desired to design an artificial line in accordance with my present invention, which shall simulate the characteristic impedance of a periodically loaded line whose specifications are as fol.- lows: An aerial line consisting of two par allel #8 B. WV. G. copper wires, loaded at intervals of 8 miles (8:8) with an initial 0.1-1- section; the distributed inductance, J, per mile of line is 0.0034 henries; the capac ity, C, per mile is 0.0092 10- farads; total resistance per mile including load coil resistance is 5 ohms; and the inductance per load coil is 0.240 henries.

The first step is to compute the c or which is equal to 0.113. Referring to equation (11) the corresponding value of w is, by interpolation, equal to 0.982. L, and C, then by equations (15) and (16) have the values, L,,:0.25S henries,

C ODOSSS X 10 farads.

The values of the elements constituting the basic structure, simulating the impedance of the loaded line beginning with a section of length (.14) X (8) miles are then, by aid of the foregoing computations and equations 5-42, found to be as follows R:1910 ohms; L,:0.522 henries; C,::0.00759 10" farads; 11 -00310 henries; C,:0.0909 10" farads; L,:0.0929 henries; C,:0.0238 10' farads.

If particularly high simulative precision is desired, the supplementary part, shown in Fig. 3, consisting of the inductance L, and capacity C, may be added to the basic structure as shown in Fig. 4. The values of L, and C, by equations (13) and 4a) are: L,:0.00090 henries; C,::6.77 10- farads.

If the consolidated form of net-work of Fig. 2 is desired, the constants L, and C, are determined by equations (45) and (46) 1 L,:0.1248 henries; and (1,:O.O188 10- far-ads.

l claim:

1. An artificial line value of simulating the charill] acteristic impedance of an actual loaded line, said artificial line comprising precomputed resistance, inductance and capacity elements having values depending on the load coil inductance, the distance between consecutive load coils, the capacity and inductance of said actual line, and the distributedcharacter of said line inductance.

2. Anartificial line simulating the characteristic impedance of an actual loaded line, said artificial line comprising precomputed resistance, inductance and capacity elements having values depending on the load coil inductance and resistance, the distance between consecutive load coils, the capacity, resistance and inductance of said actual line, and the distributed character of said line inductance.

3. An artificial line simulating the characteristic impedance of an actual loaded line, said artificial line including means having an impedance composed of" resistance and reactance components, said resistance component simulating the resistance component of the impedance of the actual loaded line, and means for neutralizing the reactance component of the impedance 'of said first named means.

4. An artificial line simulating the characteristic impedance of an actual loaded line, said artificial line including resistance and reactance elements providing impedance having a resistance component simulating the resistance component of the impedance of the actual loaded line, and means for neutrallzing the reactance component of the impedance produced by said resistance and reactance elements; whereby the joint impedance of said resistance and reactance elements and of said neutralizing means has no reactance component but has a. resistance component substantially equal to the resistance component of the impedance of said actual loaded line.

5. An artificial line simulating the characteristic impedance of an actual loaded line, the combination of meansfor simulating the reactance component of said impedance; means composed of resistance and reactance elements providing an impedance having a resistance component simulating the resistance component of the impedance of said actual loaded line; and means for neutralizing the reactance component of the impedance. produced by said. resistance and reactance elements.

6. An artificial line simulating the characteristic impedance of an actual loaded line,

i said artificial line including the combination of a resistance element in parallel with an inductance element and a condenser connected in series with each other, said combination having an impedance whose resistance component simulates the resistance component of the impedance of the actual loaded line, and means for neutralizing the reactance component of the impedance of said combination.

7 'An artificial line simulating the characteristic impedance of an actual loaded line, said artificial line comprising resistance, inductance and capacity elements simulating the resistance component of the impedance of the actual loaded line and inductance and capacity elements simulating the reactance component of the impedance of the actual loaded line, said elements having values depending on the load coil inductance, the distance between consecutive load coils, the ca pacity and inductance of said actual line, and the distributed character of said line inductance.

8. An artificial line simulating the characteristic impedance of an actual loaded line, said artificial line having a portion containing a resistance element in parallel with inductance and capacity elements connected in series with each other, and a portion in series with said other portion and consisting of an inductance element in parallel with a capacity element, said resistance, inductance and capacity elements hav ing values depending on the load c'oil inductance, the distance between consecutive load coils, the capacity and inductance of said actual line, and the distributed character of said line inductance.

9. An artificial line simulating the characteristic impedance of an .actual loaded line, said artificial line comprising a portion containing a resistance element in parallel with an inductance coil and a. condenser connected in series, said portion being connected as a whole in series with two other portions each consisting of an inductance elements bein a determined by the load coil inductance, t e distance between consecutive load coils, the capacity and inductance of said actual line, and the distributed character of said line inductance.

10. An artificial line simulating the characteristic impedance of an actual loaded line, said artificial line comprisin a portion consisting of an inductance coi in series with a condenser, said portion simulating the effect of the actual line and load resistance, a portion consisting of a resistance element in parallel with a serially connected inductance coil and condenser, and a portion consisting of an inductance coil in parallel with a condenser, said three ortions of the artificial line being connecte in series with each other, and the values of said resistance,

load coils, the resistance, capacity and inductance of said actual line, and the 'distributed character of said line inductance.

'11. An artificial line, simulating the characteristic impedance of an actual loaded line, said artificial line comprising aportion consisting of an inductance coil in series with a condenser, said portion simulating the efiect of the line and load resistance, a second portion consisting of a resistance element in parallel with an inductance coil and a condenser in series with,

each other, and two other portions each consisting of an inductance 'coil in parallel with a condenser, said four portions of said artificial line being connected in series with one another, and the values of said resistance, inductance and capacity elements being determined by the load coil inductance and resistance, the distance between consecutive load coils, the resistance, capacity and inductance of said actual line, and the distributed character of said line inductance.

12. In an artificial line simulating the characteristic impedance of an actual loaded line, a sub-combination simulating the resistance component of said impedance and comprising a portion consisting of a resistance element in arallel With an inductance coil and a con enser connected in series with each other, and a portion consisting of an inductance coil and a condenser in parallel, said portions being connected in series with each other, and said resistance, capacity and inductance elements having values dependin on the load coil inductance, the distance etween consecutive load coils, the capacity and inductance of said actual line, and the distributed character of said line inductance.

In testimony whereof, I have signed my name to this specification in the presence of two subscribing Witnesses, this 4th day of August 1915.

RAY S. HOYT. Witnesses:

GEORGE E. FOLK, JOHN R. CARSON.

one another, and the values oi said resistance, inductance and capacity elements being determined by the load coil inductance and resistance, the distance between consecutive load coils, the resistance, capacity and inductance of said actual line, and the distributed character of said line inductance. '12. In an artificial line simulating the same'page, line 116, for the symbol In testimony whereof, I have signed my name to this specification in the presence of two subscribing witnesses, this 4th day of August 1915.

' RAY S. HOYT. Witnesses:

GEORGE E. FOLK, JOHN R. GARsoN.

It is hereby certified that in Letters Patent" No. 1,16%,693, granted a nuaryil, 1916,- upon the applicati on'o f Ray S. Hoyt, of Brooklyn, New York, for an im proyencent in Artificial Lines, errors appear iii the printed specification requir- J' W I 8 read page 3, hne 7-2, equation ;r w x w e i 3 13 for read r'page 5, line {7, equation 30, for read 0,; same load coils, the resistance, capacity and in; characteristic impedance of an actual loaded 'duct'ance of said actual line, and the 'disline, a sub-combination simulating the retributed character of said'line inductance. sistance component of said impedance and 11. An artificial line, simulating the charcomprising a portion consisting of a resist- 5 acteristic impedance of an actual loaded ance element in arallel with an inductance line, said artificial line comprising aporcoil and a con enser connected in series tion consisting of an inductance coil in with each other, and a portion consisting of series with a condenser, said portion simu an inductance coil and a condenser in parlating the efiect of the lineand load reallel, said portions being connected in series 10 sistance, a second portion consisting of a with each other, and said resistance, capacresistance element in parallel with an inducity and inductance elements having Values tance coil and a condenser in series With depending, on the load coilinductance, the each other, and two other portions each -distance between consecutive load coils the consisting of an inductance 'coil in parallel capacity and inductance of said actual line,

15 with acondenser, said four portions of said and the distributed character of said line artificial line being connected in series with inductance. 40

ing correction as tollowsz Page 2, line 105,, quaftion 6, f' xi/ il d page, line 56, equation 34,1301 a? read w and-that the said Letters Patent should be read with these'corrections therein that the same may conform to they, record of the-case in thePatent Ofice: v I I I i H J I I V Signed and sealed this tfOth day of May, -A.LD., 1916. I

- air. NEWTON,

{Bimini v .w

- Abjtiag am aadwa Puma,

Corrections in L'e'tters "Patent N0. 1 ,l 67,693,

Corrections In Letters Patent No. 1,167,693.

It is hereby certified that in Letters Patent No. 1,167,693, granted January 11, 1916, upon the application of Ray S. Hoyt, of Brooklyn, New York, for an improvement in Artificial Lines, errors appear in the printed specification requiring correction as follows: Page 2, line 105, equation 6, for k/ read k=.\/

same page, line 116, for the symbol read F page 3, line 72, equation (K 2,, 2 13, for read page 5, line 7, equation 30, for G read 0,; same C 6 page, line 56, equation 34, for w read 10 and that the said Letters Patent:

should be read with these corrections therein that the same may conform to the record of thecase in the Patent Oflice.

Signed and sealed this 30th day of May, A. D., 1916.

J. T. NEWTON, Acting Commissioner of Patents.

[SEAL-1 

